Question
Hawkins Manufacturing Company produces connecting rods for 4- and 6-cylinder automobile engines using the same production line. The cost required to set up the production
Hawkins Manufacturing Company produces connecting rods for 4- and 6-cylinder automobile engines using the same production line. The cost required to set up the production line to produce the 4-cylinder connecting rods is $2200, and the cost required to set up the production line for the 6-cylinder connecting rods is $3800. Manufacturing costs are $16 for each 4-cylinder connecting rod and $18 for each 6-cylinder connecting rod. Hawkins makes a decision at the end of each week as to which product will be manufactured the following week. If there is a production changeover from one week to the next, the weekend is used to reconfigure the production line. Once the line has been set up, the weekly production capacities are 5900 6-cylinder connecting rods and 7600 4-cylinder connecting rods.
Let
x4= the number of 4-cylinder connecting rods produced next week
x6= the number of 6-cylinder connecting rods produced next week
s4= 1 if the production line is set up to produce the 4-cylinder connecting rods; 0 if otherwise
s6= 1 if the production line is set up to produce the 6-cylinder connecting rods; 0 if otherwise
A. Using the decision variablesx4ands4, write a constraint that limits next week's production of the 4-cylinder connecting rods to either 0 or 7600 units.
- x4
- s4
B. Using the decision variablesx6ands6, write a constraint that limits next week's production of the 6-cylinder connecting rods to either 0 or 5900 units.
- x6
- s6
C. Write three constraints that, taken together, limit the production of connecting rods for next week.
- x4
- s4
- x6
- s6
- s4+s6
D. Write an objective function for minimizing the cost of production for next week.
- Minx4+x6+s4+s6
Step by Step Solution
There are 3 Steps involved in it
Step: 1
Get Instant Access with AI-Powered Solutions
See step-by-step solutions with expert insights and AI powered tools for academic success
Step: 2
Step: 3
Ace Your Homework with AI
Get the answers you need in no time with our AI-driven, step-by-step assistance
Get Started